Understanding Movements in Aggregate and
Product-Level Real Exchange Rates
Ariel Burstein
yand Nir Jaimovich
zThis draft: November 2012, First draft: September 2008
Abstract
We provide new evidence on the importance of pricing-to-market in aggregate and product-level real exchange rate movements, using wholesale prices of consumer goods sold in multiple locations in Canada and the United States but produced in a common location. While movements in aggregate RERs for these goods closely track nominal exchange rates, product-level RERs across countries are four times as volatile as NERs, suggesting a limited role for sticky prices in accounting for pricing-to-market. We also show that product-level RER are twice as volatile across than within countries. We rationalize these facts using a model nesting widely-used models of pricing-to-market.
We thank Mai Bui, Jim Castillo, Yamila Simonovsky, and Daniel Weinstein for superb research assistance with our data. We also thank Andy Atkeson, Javier Cravino, Charles Engel, Emi Nakamura and David Weinstein for very useful comments.
yUCLA and NBER.
1. Introduction
One of the central questions in international macroeconomics is why relative prices across countries, as measured by real exchange rates (RERs), are so volatile over time and more speci…cally why do they so closely track movements in nominal exchange rates across coun-tries (e.g. Mussa 1986). This behavior is particularly puzzling for tradeable goods (e.g. Engel 1999). Researchers have long argued that these observations can partly be explained by the decision of individual …rms to engage in pricing-to-market — that is, to systemati-cally vary over time the markup at which they sell their output in di¤erent locations (e.g. Dornbusch 1987 and Krugman 1987).
In this paper we use detailed information on prices in Canada and the U.S. at the level of individual consumer products to document new facts on the extent of pricing-to-market in accounting for observed movements in relative prices across countries and within countries. We then use a model that nests a number of widely-used models of pricing-to-market in the literature to identify key ingredients that can account for these facts.
Our empirical work is based on scanner data for the period 2004-2006 from a major retailer that sells primarily nondurable consumer goods in multiple locations in Canada and the United States. For each product, we observe the retailer’s purchase cost from the vendor, i.e. the wholesale price, in each location and over time. We also identify the country of production of individual products that are sold in Canada and the U.S. Under the assumption that goods produced in a common location and sold in multiple locations are subject to common percentage changes in the marginal cost, movements in relative prices across locations for these goods must arise from changes in relative markups charged by producers and wholesalers. With this information, we can thus assess the extent to which movements in relative prices of individual products across locations re‡ect the practice of pricing-to-market.
We …rst constructaggregate RERsby averaging changes in relative prices between Canada and the U.S. (both prices expressed in a common currency) over a large set of products sold in Canada and the U.S. Aggregate RERs in our data closely track movements in U.S. relative unit labor costs (which are mainly accounted for by changes in the Canada-U.S. nominal exchange rate), consistent with the observation of Mussa (1986). The fact that this pattern holds for nontraded goods that are produced in each country and sold in both countries could simply re‡ect changes in relative costs across countries. The fact that this pattern holds as well for the subset of matched individual traded goods produced in a
common location and sold in both Canada and the U.S. provides direct evidence of pricing-to-market. In particular, our data suggests that for these goods markups in Canada increase systematically relative to markups in the U.S in response to the appreciation of Canada-U.S. labor costs.
Pricing-to-market in our data does not stem mechanically from large movements in nom-inal exchange rates and small movements in nomnom-inal prices in each country. To substantiate this claim, we proceed in two steps. First, we show that movements in aggregate RERs are roughly unchanged if we include or exclude observations associated with zero nominal price changes. Second, we show that nominal prices of individual products in our data change fre-quently and display a large idiosyncratic component.1 Speci…cally, changes in international
relative prices at the level of individual products,product-level RERs, are very large, roughly four times as volatile (at quarterly frequencies) as the Canada-U.S. nominal exchange rate, even for traded goods. Hence, while cross-country di¤erences in markups on average track movements in nominal exchange rates and relative labor costs, the idiosyncratic product-speci…c component of pricing-to-market is signi…cant. We also show that movements in product-level RERs between regions in the same country are substantial as well, but only roughly half as large as those between regions in di¤erent countries, and they average out when aggregated across many products. Hence, the idiosyncratic and aggregate components of pricing-to-market are more prevalent across countries than within countries.
Our empirical …ndings on pricing-to-market complement previous studies using data based on price indices from national statistical agencies or unit values at the level of goods categories or industries (see e.g. the survey in Goldberg and Knetter 1995).2 One concern
about inferring pricing-to-market at the level of individual goods using aggregate price data is that movements in international relative prices can result from di¤erences across locations in the product and quality composition of the indices, and not from changes in relative price across locations for common goods. Here we address this concern by directly using relative price movements for matched individual products sold in multiple locations.
Our …ndings are also related to a recent and rapidly growing literature documenting the behavior of international relative prices using disaggregated price data.3 Our empirical
con-1This observation is consistent with the large body of evidence on consumer prices reviewed in Klenow
and Malin (2010).
2See also Atkeson and Burstein (2008), Drozd and Nosal (2012a) and references therein.
3For example, Crucini et. al. (2005) and Crucini and Telmer (2012) document a wide distribution of
idiosyncractic deviations from the law of one price and idiosyncratic movements in product-level RERs for retail prices of narrowly de…ned product categories. Broda and Weinstein (2008) …nd similar patterns using ACNielsen’s Homescan retail price database for products with identical UPC codes but sold by multiple retailers. Gopinath et. al. (2011) document a discontinuity in wholesale and retail prices across the
Canada-tribution to this literature is to measure the extent to which movements in relative prices of matched individual products across locations speci…cally re‡ect movements in markups (pricing-to-market) by producers and wholesalers. We can do so, in contrast to those other studies, because of two unique features of our data. First, by collecting information on the country of production of individual products sold in Canada and the U.S., we can iden-tify goods that are actually traded — indeed, roughly half of our matched products are locally produced for domestic consumption in each country in spite of belonging to tradeable product categories. Second, by observing wholesale prices we can more accurately measure movements in relative markups at the producer and wholesale level than if we used retail prices, which contain a signi…cantly higher non-traded distribution component. For traded goods produced in a common location, under the null that changes in marginal cost are independent of destination location, we can infer changes in relative markups across location from movements in relative prices. In contrast, for goods produced in di¤erent locations, movements in relative prices arise from movements in markups and from movements in pro-duction and distribution costs across locations.4 Distinguishing between these two source of
price changes is important from a normative perspective since changes in prices that re‡ect movements in costs are e¢ cient while changes in prices that re‡ect movements in markups are ine¢ cient.
In contemporaneous work to ours, Fitzgerald and Haller (2012) …nd that pricing-to-market by Irish producers is signi…cant in response to movements in the Euro/Sterling exchange rate using domestic and export prices at the plant level from the PPI monthly survey.5 In contrast, Berman, Martin, and Mayer (2012) …nd that the degree of
pricing-to-market based on annual 8-digit unit values for French exporting …rms is much smaller, but varies systematically across …rms consistent with the models of pricing-to-market that we describe below. In addition to documenting a high degree of pricing-to-market using weekly and quarterly prices of matched individual products, we show that there is a large component of pricing-to-market that is uncorrelated with movements in the nominal exchange rate, and that pricing-to-market is more prevalent across than within countries.6
U.S. border for products with identical UPC codes using our same dataset.
4Amiti, Itskhoki, and Konings (2012) use unit values for Belgian …rms to show that exchange-rate
pass-through into costs has a signi…cant role in accounting for pass-pass-through into prices. We identify the component of pass-through stemming from variable markups by focusing on movements in relative prices across locations for identical traded goods.
5Prices used in Fitzgerald and Haller (2012) are signi…cantly stickier than ours, which may re‡ect the
survey nature of their data and di¤erences in price stickiness between industrial goods and consumer goods.
6In related work, Goldberg and Hellerstein (2011), Hellerstein (2008), and Nakamura and Zerom (2010)
Our empirical …ndings raise the following questions: Why do relative markups systemat-ically track movements in relative costs across countries, even if nominal prices of individual products change frequently and by large amounts? Why is pricing-to-market more preva-lent across countries than within countries? What is the role of the international border in giving rise to pricing-to-market across countries? We present a simple partial equilibrium framework that allows us to provide some answers to these questions.
The framework encompasses a number of widely-used static models of international pric-ing with variable markups and ‡exible prices (for a recent review of these models, see Burstein and Gopinath 2012), which build on the pricing-to-market models pioneered by Dornbusch (1987) and Krugman (1987).7 We extend these models in two ways. First, we introduce
idiosyncratic time-varying cost and demand shocks in order to account for movements in product-level RERs (for traded goods) that are larger than movements in relative unit labor costs and aggregate RERs. Second, we introduce multiple regions within countries in order to account for movements in relative prices within and across countries. Within this class of models, we provide analytic expressions to isolate key forces that can rationalize our empir-ical …ndings. We also use our model to discuss what our …ndings on pricing-to-market for traded goods imply for the extent of segmentation of markets across and within countries. In doing this, we complement the insights of Engel and Rogers 1996, Gorodnichenko and Tesar 2009, and Gopinath et. al. 2011 that do not distinguish between goods produced in one location and sold in multiple locations and those that are not.
In our model, movements in product-level RERs for traded goods produced in a common location and sold in multiple regions result from a combination of (i) region segmentation, which induces di¤erences across regions in a product’s price sensitivity of its demand elastic-ity (which determines the markup elasticelastic-ity), and (ii) less-than perfectly correlated demand shocks (or other shocks that move markups) across regions for individual products. Our model can account for our empirical fact that product-level RERs are more volatile across regions in di¤erent countries than within countries if either (i) regions are more segmented between countries than within countries, or (ii) demand shocks for individual products are less correlated between countries than within countries. Hence, one message from our model for empirical research is that the observed variation across regions in the volatility of product-pass-through. De Loecker et. al. (2012) infers markups using producer prices and production function estimates. In contrast, we do not impose a theoretical structure to the data and instead use variation in relative wholesale prices for products produced in a common location and sold in multiple locations to quantify the extent of changes in relative markups across locations.
7See e.g. Drozd and Nosal (2012a,b) and Ravn, Schmitt-Grohe and Uribe (2007) for analysis of
level RERs can be used to gauge the degree of segmentation within and between countries, only if the correlation of demand shocks across regions (or other shocks to markups) can be measured and "controlled" for.
In our model, the close comovement between relative unit labor costs and aggregate RERs for traded goods produced in a common location and sold in multiple regions results from a combination of (i) a demand featuring large markup elasticities to prices and (ii) movements in relative aggregate prices between regions that closely comove with relative unit labor costs, due to regional segmentation. Our model can account for our empirical fact that movements in aggregate RERs are smaller within countries than between countries if either (i) movements in unit labor costs are relatively smaller across regions within countries than between countries, or (ii) regions are less segmented within countries than between countries. Hence, one can use the observed variation across regions in movements of aggregate RER to gauge the degree of segmentation across regions within and between countries, only if one can identify and "control" for changes in relative costs across regions within countries that are comparable to changes in relative costs across countries (e.g. movements in nominal exchange rates).
Our paper is organized as follows. Section 2 describes our data. Section 3 reports our main …ndings on international price movements. Section 4 presents the framework to interpret our empirical facts. Section 5 concludes.
2. Data Description
Our analysis is based on scanner data from a major food and drug retail chain that operates hundreds of stores in Canadian provinces and U.S. states.8 The Canadian stores are located
in British Columbia, Alberta and Manitoba, and the U.S. stores are in multiple states cov-ering a large area of the U.S. territory. We have weekly data over the period 2004-2006, covering roughly 60;000 products de…ned by their universal product code (UPC).
The retailer classi…es products as belonging to one of200categories. We exclude from our analysis “non-branded” products such as fruits and vegetables, deli sandwiches, deli salads, and sushi because for these products information on the identity and country-of-origin of the producer is harder to obtain. For the same reason, we abstract from retailer brands within each product category. We also leave out magazines because advertising revenues account for a substantial share of the publisher’s total revenues. This leaves us with 71 8Data from this retailer have been used by Chetty et. al. (2008), Eichenbaum et. al. (2011), Einav et.
product categories satisfying the data requirements discussed below. These categories include beverages, cleaning products, personal care, and processed food. Since our …ndings do not vary systematically by product categories, we report aggregate statistics across all products with available data.
For each store we have weekly information on quantities sold, sales revenue (in local currency), and the retailer’s total cost (in local currency) of purchasing the goods from the vendors, net of discounts and inclusive of shipping costs. Following Eichenbaum et. al. (2011), we divide revenues and costs by quantities sold to obtain a measure of weekly retail and wholesale prices, respectively. At any point in time, the wholesale price is viewed by the retailer as measuring the replacement cost of an item. As discussed in Eichenbaum et. al. (2011), the retailer uses this cost measure in its pricing decisions and in its calculations of variable pro…ts per good.
In order to measure the extent of pricing-to-market, we focus our analysis primarily on wholesale prices (rather than retail prices). While wholesale prices are the closest measure of producer prices in our data, they are not free of local wholesale distribution costs. Hence, we cannot separately infer the extent of variable markups at the producer and wholesale level from distribution costs at the wholesale level. However, local distribution services are, on average, modest at the wholesale level, and substantially less sizeable than at the retail level. For example, based on information from the U.S. wholesale and retail census, for groceries and related products the average 1998-2006 gross distribution margin (as a percentage of wholesale sales) is only16%at the wholesale level (the combined retail and wholesale margin as a percentage of retail sales is roughly40%).9 In Section 3.3, we brie‡y report our central
empirical …ndings based on retail prices.10
2.1. Aggregation across space and time
Aggregation across space The retail chain groups di¤erent stores into relatively
con-centrated geographic areas within a province or a state that share a common pricing policy, which we denote as apricing region. Based on information from the retailer and on our own calculations, the locations of the stores with products satisfying our data requirements can
9This information is available at www.census.gov/econ/www/retmenu.html , which was previously used
in Burstein, Neves and Rebelo (2003).
10Given that our data covers one single retail chain, we are not able to measure the extent of
pricing-to-market by producers and wholesalers across di¤erent retail chains for common products (see e.g. Nakamura 2008 for a discussion of retail pricing within and across retail chains). If pricing-to-market by producers and wholesalers is more prevalent across di¤erent retailer chains than across di¤erent locations within a single retail chain, then our results understate the extent of pricing-to-market in the data.
be mapped into14pricing regions in Canada and85pricing regions in the U.S. We choose to focus on these as our geographic unit because, given the retailer’s pricing policy, retail and wholesale prices are very similar across stores within pricing regions. That is, considering all individual stores within each pricing region would substantially increase the size of our dataset without essentially adding new information.
We construct a weekly wholesale price for each pricing region as the median wholesale price across stores within the pricing region. Our baseline statistics are computed for the 5
pricing regions in British Columbia in Canada, and14pricing regions in Northern California in the U.S. These regions are roughly comparable in geographic scope and cover the stores where the country of production was identi…ed. In the sensitivity analysis, we report our statistics based on all pricing regions in our data and other variations in the geographic scope.
As we document below, there is some variation (both in levels and in changes) in wholesale prices of individual products across pricing regions. As we learnt from interviews with managers at the retailer, this is because vendors charge di¤erent prices for the same product in di¤erent regions. Part of this regional variation in prices may arise from di¤erences in scale combined with non-linear pricing by vendors. Our goal, however, is to document the extent of movements in relative wholesale prices for exported goods across locations (i.e. pricing-to-market), without taking a stand on the form of contractual arrangements between the retailer and the vendors, which would require detailed information that is currently unavailable for the large number of products in our sample.11
Aggregation across time Our baseline statistics are based on prices at quarterly
fre-quencies. For each product, these are constructed as unweighted averages of weekly prices within the quarter.12 By averaging prices across weeks within quarters, we smooth out some of the highly temporary price changes that result from sales and promotions. As discussed in Section 3.3, relative prices across locations are more volatile at weekly frequencies than at quarterly frequencies. Therefore, our baseline statistics based on quarterly prices understate the extent of pricing-to-market in our data. We also calculate mode prices (the most com-mon weekly price within each quarter) to perform sensitivity analysis on the role of sticky prices in accounting for movements in RERs.
11This information is not only unavailable to us, but also to the managers at the retailer that we
inter-viewed.
12Constructing quarterly prices as quantity-weighted averages (rather than unweighted averages) of weekly
2.2. Matching products
In order to measure movements in relative prices between pairs of regions (within countries or across countries), we must …rst match products that are sold in both regions. For pairs of regions within the same country, we match products that have common UPC codes in both regions. For pairs of regions in di¤erent countries, we proceed in two steps.
First, we match products that have identical UPC codes in Canada and U.S. As reported in Table 1, this gives us 539 identical UPC product matches across countries (for which we have country of production information described below) in British Columbia and Northern California, and987 across all pricing regions.
Second, since our emphasis is on understanding price changes over time, as opposed to di¤erences in price levels at a point in time, we construct a broader set of internationally matched products beyond products with identical UPCs. To do so, we consider items within product categories that have di¤erent UPC codes but share, in both countries, the same brand, manufacturer, and at least one additional characteristic in the product description. This procedure does not require that matched products share a common size and exact product description. These broader matches include, for example, “Schweppes Raspberry Ginger Ale 2Lts” in Canada with “Schweppes Ginger Ale 24 Oz” in the U.S., “Purex Baby Soft” in Canada with “Purex Baby Soft Classic Detergent” in the U.S., “Crest toothpaste sensitivity protection”in Canada with “Crest sensitivity toothpaste whitening scope”in the U.S., and “Gatorade strawberry ice liquid sports drink” in Canada with “Gatorade sports drink …erce strawberry” in the U.S. Individual products can be matched more than once. For example, Coca-Cola 2lt in Canada is matched with Coca-Cola 12 Oz and Coca-Cola 24 Oz in the U.S. This process yields 7219 product matches across countries in British Columbia and Northern California, and 11872 across all pricing regions. As long as two products that are matched and produced in a common location share a commonpercentage change in marginal cost for sales in Canada and the U.S., changes in relative prices across locations can be interpreted as movements in relative markups by individual producers (i.e., pricing-to-market).
To show that our main …ndings on movements in RERs are not driven by matches with non-identical UPCs, we report separately results based on broad matches and results based only on identical product matches (for statistics for which we have su¢ cient observations). While di¤erences in price levels across international regions are greater if we consider our broad set of matches (since these include e.g. products of di¤erent size), our …ndings on movements over time in relative prices are largely robust to these two alternative matching
procedures.
2.3. Inferring country of production
Next, we identify the country of production for matched products sold in Canada and the U.S. For each of our matched products, our procedure is as follows. First, in the U.S., we use the country-of-origin label information that is available in the retailer’s online store for sales in Northern California.13 Second, in Canada, given that the country-of-origin information is
not available on-line, two research assistants physically visited the retailer store in Vancouver, British Columbia, and recorded the country-of-origin label information.14 Third, our research
assistants veri…ed the label information by calling many of the individual manufacturers. This procedure was carried out during the months of May-June 2008.
We group our matched products into four country-of-production sets. The …rst set con-sists of matched products that are produced in the U.S. for both U.S. and Canadian sales, such as Pantene shampoo, Ziploc bags, and Rold Gold Pretzels. The second set consists of matched products that are produced in Canada for both U.S. and Canadian sales, such as Sapporo beer, Atkins advantage bar, and Seagram whisky. The third set consists of matched products that are produced in the U.S. for U.S. sales and in Canada for Canadian sales, such as Coca-Cola, Haagen-Dazs ice-cream, Yoplait yoghurt, and Bounce softener. The fourth set consists of matched products that are produced in other countries for U.S. and Canadian sales, such as Myojo instant noodles (Japan), Absolut vodka (Sweden), and Delverde pasta (Italy).
There are two important caveats to our approach. First, a product’s country of pro-duction may vary across regions within the U.S. and Canada. To address this concern, in our baseline results we only include the pricing regions in British Columbia and Northern California, where the information on country of production was obtained.
Second, a product’s country of production may vary over time. To address this concern, between February 2010 and April 2010 (roughly two years after our …rst survey), we
re-13According to the U.S. Federal Trade Commission’s rules, for a product to be labelled ‘Made in USA’,
the product must be “all or virtually all” made in the U.S. In Canada we do not know of such a legal label requirement. If there was a bias in reporting goods as locally produced when they are not, then products that are labelled as foreign produced would be very likely to be so. Hence, given that our inference on pricing-to-market is based on goods that are produced in a common country, we believe that for these goods the country-of-origin information is quite accurate. Note also that foreign produced goods can potentially have a local packaging component. These local distribution components would have to be extremely large to account entirely for the large movements in RERs observed in our data.
14Given that our retail chain does not sell liquor products in Vancouver, we obtained their
country-of-origin information from other stores. We use this information when examining price movements of liquor products in other Canadian cities.
sampled the country of origin in the U.S. Out of the13718products in the U.S. with available information on country of origin in 2008 (these products are not all matched with products in Canada),13120products (roughly95%) did not change their country of origin between 2008 and 2010,411 products (roughly 3%) had changed their country of origin, and287 products (roughly2%) had been discontinued. This information complements informal evidence based on interviews with managers of the retail chain suggesting that there is little variation over time in the country of production of continuing products.
2.4. Descriptive statistics on matched products
Table 1 provides descriptive statistics for the set of matched products that we use in our analysis. We report the information separately for identical and broader matches, for pricing regions in British Columbia and Northern California and for all regions. The set of identical matches covers roughly 5% of the retailer’s total sales (evaluated at wholesale prices) over our set of product categories (Row 1), and the set of broader matches covers roughly50% of total expenditures in Canada and36% in the U.S. (Row 12).15
Rows 2-4 and 13-15 report expenditure shares by country of production. There is a signif-icant degree of home bias in consumption. In particular, based on our broad set of matches, roughly 90% of expenditures on our set of matched products in the U.S. are domestically produced, while imports from Canada and the rest of the world (ROW) account for only
1% and 10% of expenditures, respectively. In Canada, roughly two-thirds of expenditures on our set of matched products are domestically produced, while imports from the U.S. and ROW account for 30% and 3% of expenditures, respectively.16 The large size of the U.S.
economy relative to Canada is re‡ected in the smaller share of U.S. imports from Canada in comparison to the share of Canadian imports from the U.S.
Rows 5-9 and 16-20 report the number of matched products, divided into our four country-of-production sets. Roughly half of the matched products are produced in the U.S. for both U.S. and Canada sales (U.S. exports). Roughly 30% of our set of broad matches are domestically produced in each country. The number of matched products that are exported either by Canada or by ROW is signi…cantly smaller than the number of those that are
15We do not cover 100% of the expenditures for the following three reasons. First, we abstract from
retailer brands. Second, many products cannot be matched across Canada and the US. Third, for some of the matched products we lack information on the country of production.
16Our data provide a good representation of bilateral trade shares for Canada and U.S. based on more
aggregate data. In particular, the import shares reported in Table 1 are similar to OECD-based import shares for comparable industries including beverages, chemicals, food products, and tobacco over the period 1997 2002.
exported by the U.S. or domestically produced. Therefore, our statistics for Canadian and ROW exports are more prone to small sample limitations.
Table 2 presents some basic statistics on the extent of price dispersion of wholesale prices of matched individual goods across locations. In particular, we calculate the average and medianabsolute logarithmic di¤erences in quarterly price levels across pricing regions over all time periods. We present these statistics separately for our set of identical and broad product matches, and for all pricing regions and for pricing regions only in British Columbia and Northern California. Based on identical product matches, the average (median) absolute log price di¤erence within countries is relatively small: 0:049 (0:02)between all pricing regions in the U.S., and0:029(0:011) between all pricing regions in Canada. These within-country price dispersion measures are very similar if we consider our broader set of product matches and if we consider only pricing regions in British Columbia and Northern California. The extent of price dispersion is much larger across countries. Based on the set of identical product matches, the average (median) absolute log price di¤erence between all pricing regions in Canada and the U.S. is 0:23 (0:19). Price di¤erences are larger if we consider our broad set of product categories (the average and median of absolute price di¤erences are roughly twice as large). This is not surprising since, recall, broad product matches do not necessarily share a common size and exact product description. Below we show, however, that our statistics on movements in product-level RERs do not di¤er signi…cantly if we focus on exact or broad product matches.
3. Aggregate- and product-level real exchange rates
In this section we construct and establish our central empirical …ndings on movements in aggregate- and product-level RERs. We …rst show that movements in Canada-U.S. aggregate RERs closely track relative unit labor costs. For exported products that are produced in a common country and sold in both countries, this is evidence of pricing-to-market by individual producers or wholesalers. Next, we show that these movements in relative prices are not the result of sticky nominal prices and volatile nominal exchange rates. Instead, product-level RERs are very volatile because price changes are frequent, large, and not very correlated across international locations. Next, we show that movements in relative prices are larger between countries than between pricing regions of the same country. We provide extensive robustness checks to these three …ndings.
Constructing product-level and aggregate RERs We denote individual products by n 2 , time periods by t = 1; :::; T, and regions by r = 1; :::; R. Regions r = 1; :::; R1 are
located in Canada, regionsr =R1+ 1; :::; R2 are located in U.S., and regionsr =R2+ 1; :::R
are located in the rest of the world (ROW). We typically indicate by r and r0 the pricing regions where goods are sold, and we indicate by i and j the regions where goods are produced. We denote byErr0tthe nominal exchange rate between regionsr and r0 in period
t(units of currencyr0 per unit of currencyr). For regions within the same country,E
rr0t = 1.
The price in region r in periodt for product n produced in region i is denoted by Pnirt.
We denote by Qnijrr0t = PnirtErr0t=Pnjr0t the price of product n in region r produced in region i relative to the price of product n in regionr0 produced in region j, both expressed
in the same currency. We refer to the relative price of individual products across regions as product-level RERs. The log change in the product-level RER is given by:
qnijrr0t= pnirt+ err0t pnjr0t,
wherex= log (X), and xnirt = log (xnirt) log (xnirt 1). For products that are produced in
a common location i and share a common percentage change in marginal cost, qniirr0t 6= 0
indicates that producers and wholesalers price-to-market by varying their markups across locations r and r0, as we show in our model in Section 4. Throughout our analysis we trim our data by excluding observations for which quarterly changes in product-level RERs are larger than 100 log points, i.e. j qnijrr0tj >1, which amount to less than 0:1% of the total
number of observations.
Aggregate RERs are constructed by averaging changes in product-level RERs over a large set of matched individual products and pairs of regions. We are particularly interested in calculating aggregate RERs across goods produced in a common location and sold in multiple locations. The change in the Canada-U.S. aggregate RER between periods t 1 and t over a set of products produced in locationi2I and sold in multiple regions in Canada and U.S. is de…ned as:
qt= X
i2I X n2 i
snt medianf qniirr0t,g
r=A;:::;R1;r0=R1+1;:::;R, (3.1)
where i is the set of goods produced in locationiand sold in multiple destinations. For the
set of production locationsIwe use either all U.S. exported products or all exported products (Canada, U.S., and ROW). Expression (3.1) indicates that for each matched product, we calculate the median change in product-level RERs over pairs of regions in the two countries where the good is sold. The weights of each product, snt, are equal to expenditures in
product n in period t relative to expenditures in all products sold in periods t 1 and t, where expenditures are summed over all time periods and all regions in Canada and U.S. By averaging-out the idiosyncratic changes in product-level RERs, aggregate RERs capture the time-varying components that are common to many products.17 We also construct Canada-U.S. aggregate RER for goods produced domestically for sales in each country, and intranational aggregate RERs across regions within countries.
3.1. Aggregate real exchange rates
Figures 1 and 2 and Table 3 report cumulative movements of aggregate RERs between our sample period, 2004 2006, for di¤erent set of matched products, as well as the cumulative increase in relative unit labor costs between Canada and the U.S. as constructed by the OECD. Over this time period, relative unit labor costs increased in Canada by roughly15%, mainly accounted for by an appreciation of the Canadian dollar relative to the U.S. dollar of a similar magnitude.
Over this period, prices in Canada rose substantially relative to prices in the U.S., leading to the observed increase in Canada-U.S. aggregate RERs in the four panels in Figure 1. Based on the broad set of product matches and the pricing regions in British Columbia and North California, the aggregate RER rose by roughly 14:3% for all exported products (Panel A),
11:8%for only U.S. exported products (Panel B), and12:2%for domestically produced goods (Panel B). The rise in Canada relative to U.S. prices is very similar if we consider all pricing regions instead of only British Columbia and North California (Panel C).
To illustrate that the large changes in aggregate RERs for exported products are not driven by our choice of broad product matches we proceed as follows. We …rst choose prod-uct categories that have su¢ ciently large observations of both broad and identical prodprod-uct matches. We identify …ve such product categories with U.S. exported products.18 Panel D in Figure 1 and Table 3 display the cumulative change in the aggregate RER using identical product matches and broad product matches for these …ve product categories. Based on
17We use the median, rather than the mean change in product-level RERs across regions because the
because the resulting movements in aggregate RERs constructed in that way are smoother. We do not consider separately aggregate RERs for Canada and ROW exports because the number of products exported by these countries is too low to smooth-out the idiosyncratic movements in product-level RERs. We also constructed aggregate RERs based on aggregate price indices de…ned as weighted-average changes in prices over a set of products and regions within a country, following the procedure of the U.S. Bureau of Labor Statistics. The resulting movements in aggregate RERs are very similar to those constructed using (3.1).
18To choose a category, we require a minimum of 10 identical product matches and 10 broad product
matches over the 12 quarters of the data. There are only 5 categories that satisfy this constraint because the number of matched products with identical UPC codes is signi…cantly smaller than the number of broad matched products (see Table 1) .
identical product matches, the Canada/U.S. aggregate RER rose by 13% over our sample period, while based on broad product matches the aggregate RER rose by 15:8%. Hence, aggregate RER based on broad product matches track quite closely aggregate RER based on identical UPC codes for comparable product categories.
We conclude from Figure 1 and Table 3 that, on average, wholesale prices for matched products rose systematically in Canada relative to the U.S. in response to the increase in Canada-U.S relative unit labor costs, even for exported products produced in one country and sold in both Canada and U.S.
Intra-national aggregate RERs We construct intra-national aggregate RERs, averaging
movements in product-level RERs across matched products for all pairs of pricing regions within Canada and within the U.S. (using expression 3.1). Results are reported in Panels A and B in Figure 2 and in Table 3. Changes in intra-national aggregate RERs are signi…cantly smaller than change in international aggregate RERs: for all products, the cumulative change is roughly 0 within Canada and within U.S. These statistics are very similar if we focus on exported or domestic goods. Intra-national aggregate RERs are roughly constant over time because idiosyncratic movements in product-level RERs wash-out, nominal exchange rates within countries are constant Err0t = 1, and region-speci…c shocks within countries play a
minor role in shaping movements in relative prices, on average, across regions. In comparison, the large observed changes in relative costs across countries (which in our data are mainly accounted for by changes in nominal exchange rates) are central in driving movements in aggregate RERs across countries.
Sticky prices and aggregate RERs If prices are sticky in the buyer’s currency (local
currency pricing), an appreciation of the Canadian dollar mechanically increases Canadian prices relative to U.S. prices measured in the same currency, as observed in Figures 1 and 2. Individual wholesale prices in our data, however, move quite frequently. For our same retailer, Eichenbaum et. al. (2011) calculate the degree of price stickiness based on the raw weekly data across individual stores in the U.S. The probability of a weekly wholesale U.S. dollar price change across all product categories is0:49in the U.S., which implies that the expected duration of wholesale prices is 0:16quarters. We complement this information by calculating the degree of price stickiness based on locations in Canada, which is very similar to that for the U.S. Moreover, the fraction of weekly observations across our matched products in which either the Canadian price or the U.S. price changes is even higher at 0:72
(and 0:73 for only exported products). This implies that, on average, the probability that Canadian and U.S. prices remain both unchanged (as required by the sticky local prices hypothesis above) over a period of 13 weeks (a quarter) is roughly 0:2813 which is close to
zero.
We also measure price stickiness based on modal local-currency prices, the most common price across weeks within each quarter. Eichenbaum et. al. (2011) refer to these modal prices as reference prices, since they …lter-out sales or other highly temporary variation in weekly prices. They report that reference prices are much stickier than weekly prices. For example, the probability of a change in the quarterly reference wholesale price across all product categories is 0:49in the U.S., implying an expected duration of2:2 quarters.19
We now gauge the role of price stickiness in shaping movements in aggregate RERs. We do not identify changes in nominal prices either from highly temporary changes in weekly nominal prices or from changes in average quarterly prices since it takes a single change in weekly prices within the quarter to change this average price. Instead, to be conservative, we identify changes in nominal prices from changes in the more sticky reference (modal) quarterly prices de…ned above. We re-calculate movements in aggregate RERs including changes in product-level RERs in which the modal price (in local currency) changes in either Canada or the U.S. That is, in equation (3.1), for each time period t we only include products n and pairs of location r; r0 in which either the Canada or the U.S. modal price change between t 1 and t. Once we identify these observations in which modal nominal prices change, we calculate aggregate RERs using product-level RERs based on average quarterly prices to make them comparable to our baseline statistics.
Figure 2 and Table 3 report the results from these calculations. The cumulative change in the aggregate RER over our sample period is extremely similar if we include or exclude product-level RERs associated with sticky modal prices. For example, for all exported products, the aggregate RER increases by 14:3% including all price observations and14:2%
if we exclude observations with unchanged modal prices.
For robustness, to further assess the role of small price changes in shaping movements in aggregate RERs, we report changes in aggregate RER calculated using observations in which the sum of the absolute change of Canada and U.S. local-currency modal prices is
19Reference prices are even more sticky at the retail level. While the probability of a weekly retail price
change is0:43(expected duration of0:18quarters), the probability of a change in the reference price is0:27 (expected duration of3:7quarters). For comparable categories of goods, the frequency of price adjustment for wholesale prices in our data (reported in Eichenbaum et. al. 2011) is similar to that for U.S. import prices reported in Gopinath and Rigobon (2008).
larger than 1% or 2% (instead of using a threshold of 0%). The cumulative increase in the aggregate RERs is only2%lower when we exclude product-level RERs associated with small modal price changes.
In sum, the presence of sticky local currency prices has at most a limited role in accounting mechanically for the two-years, steady rise in Canada-U.S. aggregate RERs. This is because, …rst, prices in our data change quite frequently, and second, relative prices associated to non-sticky local-currency prices track closely the movements in relative unit labor costs.20
3.2. International product-level real exchange rates
We now show that, underlying the smooth rise in Canada-U.S. aggregate RERs and the largely constant intra-national aggregate RERs reported in Figures 1 and 2 and in Table 3, there are very large idiosyncratic movements in product-level RERs.
To …x ideas, Panel A and B in Figure 3 depicts movements of prices and product-level RERs for one identically-matched product in our sample. The product belongs to the product category “Tea” and is produced in the U.S. for sales in both the U.S. and Canada. Panel A displays the 11 quarterly growth rates of prices (all expressed in U.S. dollars), Pnirt, in
three pricing regions: two regions in the U.S. (both in Northern California), and one region in Canada (in British Columbia). Panel B displays the percentage change in the relative price between the two U.S. regions and the relative price between one region in the U.S. and one in Canada. Panel B also displays quarterly changes in relative unit labor costs between Canada and the U.S. One can observe for this particular product that relative prices between Canada and the U.S. change by large magnitudes over time, more so than relative unit labor costs.
Panels C and D in Figure 3 presents histograms of the movements in international product-level RERs between British Columbia and Northern California like those displayed in Panel B, but now for all exported matched products across all pairs of regions. Panel C considers our broad set of matched products, while Panel D considers our set of identically matched products. Observe that in all panels, movements in product-level RERs are quite large.
To quantify this information, we construct a measure of volatility of international product-level RERs (i.e. between regions of di¤erent countries). The international variance of product-level RERs over a set of products produced in a common location i2I and sold in
20The replacement bias studied in Nakamura and Steinsson (2011) and Gagnon, Mandel and Vigfusson
(2012) is less likely to be of a concern in our data than in the BLS data because prices in our data change quite frequently.
multiple regions is de…ned as Varinter =X
i2I X n2 i
R1
X r=1
R X r0=R1+1
T X
t=2
1
n qniirr0t qinter
2
, (3.2)
where qinter denotes the average change in relative prices over these products, regions,
and time periods, and n denotes the number of observations over which this statistic is evaluated. We report standard deviation of international RERs, pVarinter, instead of the variance, to facilitate the comparison of our results with standard measures of nominal and real exchange rate volatility. For the set of production locations I we use either all exported products, U.S. exported products, Canada exported products, or ROW exported products. We also construct this statistic over products produced domestically and sold in each country. We report in Tables 4 and 5 our statistics for the various country-of-production sets, for identical and broad product matches, for British Columbia/ North California and for all pricing regions, and other sensitivity cases discussed below.
Product-level RERs across countries are very volatile not only for matched products that are domestically produced in each country, but also for matched products that are produced in one country and exported to other countries. In particular, based on our set of broad product matches in British Columbia and North California (Panel A of Table 4), the international standard deviation of product-level RERs is equal to 11:2% for all exported products,10:9%for U.S. exports,17:2% for Canadian exports,13:1% for ROW exports, and
13:5% for matched products that are domestically produced in each country. Product-level RERs are also very volatile if we only consider identical product matches (e.g. 13:2% for all exported products in Panel B of Table 4), and if we consider all pricing regions (e.g. 13:1%
for all exported broad matched products, see Panel B of Table 5). To put these …gures into perspective, the standard deviation of quarterly changes in the Canada-U.S. relative unit labor costs, nominal exchange rate, and the CPI-based RER between 1998 and 2007 is roughly 3%.
The high volatility of product-level RERs is not mechanically driven by exchange rate movements and sticky local currency prices. To observe this, we calculate two statistics. First, we calculate changes in product-level RERs using local currency prices without con-verting international prices to a common currency. For all exported products, the standard deviation of international product-level RERs falls only from 11:2% to 10:8% (Panel C in Table 5). Second, we calculate changes in product-level RERs excluding those observations in which both the Canadian and the U.S. modal prices change (Rows 4 and 12 in Table 4). For all exported products, the standard deviation of international product-level RERs
rises from11:2%to11:9%.21 These two observations should not be very surprising given our previous results that individual wholesale prices in our data move quite frequently and by large magnitudes.
Product-level RER’s are volatile because price changes are not very correlated between countries. To see this, we can express (3.2) as:
Varinter = VarCanP +VarUSP 1 2 Var P Can
0:5
VarUSP
0:5
VarCanP +VarUSP Correl
Pinter !
, (3.3)
where Varj P denotes the variance of price changes Pnirt over the various pricing regions in
countryj =Canada or U.S. and Correlinter denotes the correlation of price changes between
pairs of regions in Canada and U.S. In our data, the variance of U.S. dollar denominated nominal price changes, is roughly equal in the U.S. and Canada, , Var P
Can ' VarUSP =Var P.
For all exported products, for example, the standard deviation of price changes is 7:8% in Canada and8:1% in the U.S. Hence, Varinter is roughly equal to 2Var P 1 Correl Pinter . If price changes are perfectly correlated across countries, then Varinter = 0. If price changes
are uncorrelated across countries, then Varinter = 2Var P.
Tables 4 and 5 report the value of Correl Pinter for the various country-of-production sets, for the set of broad and identical product matches. We can see across all rows and columns that Correl Pinter is very low, even for exported products. For example, for all exported broad matched products (Row 8, Panel A in Table 4), Correlinter = 0:065.
Inter- and intra-national product-level real exchange rates For our selected “Tea”
product in Figure 3, one can observe that relative prices are more volatile between the pricing regions in British Columbia and Northern California than between the two pricing regions in Northern California. More generally, Figure 4 displays histograms of relative price movements across our entire set of broad matched products, between pairs of pricing regions in British Columbia and Northern California, as well as between pairs of pricing regions within British Columbia and within Northern California. Movements in product-level RERs are larger between countries than between pricing regions of the same country.
To quantify this pattern, we de…ne the intra-national (i.e. between regions of the same country) variance of product-level RERs for goods produced in a common location in country iand sold in multiple locations in countryj =Canada or U.S., analogously to Varinter in (3.2), 21If we exclude observations for which the sum of the absolute change of Canada and U.S. local-currency
modal prices is less than2%(Rows 5 and 13 in Table 4), the standard deviation of international product-level RERs further rises to13:7%.
as:
Varintraj =X i2I
X n2 i
X r2R~
X r02R~
T X
t=2
1
n qniirr0t qintra
2
, (3.4)
where R~ = f1; :::; R1g when j =Canada and R~ = fR1 + 1; :::; Rg when j =US. Tables 4
and 5 report the standard deviation of intra-national product-level RERs,
q
Varintraj , for our various country-of-production sets and product matches.
Product-level RERs are almost two times as volatile across countries than within coun-tries. For example, based on our broad set of product matches and pricing regions in British Columbia and Northern California (Rows 1 and 2, Panel A in Table 4), the standard devia-tion of product-level RERs for all exported products is4:2%within Canada,5:7%within the U.S., and11:1% across countries. If we consider only identical product matches (Rows 9 and 10, Panel B in Table 4), intra-national product-level RERs are slightly more volatile (6:2%
and 7:5%, respectively), but still substantially less volatile than inter-national product-level RERs.22
These statistics are constructed based only on the pricing regions in British Columbia and Northern California. If we include all pricing regions (Rows 1 and 2, Panels A and B in Table 5) intra-national product-level RERs are more volatile (6% in Canada and 8% in the U.S. for exported broad product matches) but still less volatile than international product-level RERs (13:1%). To control for variation in distance across regions, we follow the literature (e.g. Engel and Rogers 1996) and consider the following regression. The dependent variable is the standard deviation of product-level RERs across all pairs of pricing regions within and across countries for identical matches (there are 964;179 upc/pair of regions for which we calculate this measure). The independent variables include a constant, the logarithm of distance between the pairs of regions, product-category dummies, and a dummy that equals one if the two regions lie in di¤erent countries. The distance coe¢ cient is positive and signi…cant (the coe¢ cient equals0:004 with a t-stat of 70), suggesting that regions that are farther apart experience larger deviations from relative PPP. More importantly, the dummy coe¢ cient is equal to 5:4% and statistically signi…cant (a t-stat of 357). Note that the value of this dummy coe¢ cient is very similar to the di¤erence in the standard deviation of
22Our …nding thatV arintra
U S > V arCanintraechoes the …ndings in Gorodnichenko and Tesar (2009) who use more
aggregated price data. Broda and Weinstein (2008) report a higher level of Varintra
Can and a smaller di¤erence
between Varintra
Can and Varinter than we do. Even though they use retail prices while we use wholesale prices,
our results are largely unchanged with retail prices. Two other di¤erences between their data and ours are: (i) prices in their data are averages across multiple retailers, which can lead to a higher Varintra
Can through
changes in composition of retail sales over time, and (ii) U.S. prices in their data are averages of prices across multiple regions, which can reduce Varinter by eliminating the region speci…c component of U.S. price
inter- and intra-national product- level RERs based only on data from British Columbia and Northern California. This con…rms our previous …ndings that pricing-to-market is roughly twice as prevalent across countries than within countries.
Relative prices are more volatile across countries than within countries because price changes are more correlated across regions within countries than across pricing regions be-tween countries. To see this, we can express the ratio of inter- to intra-national RER variances de…ned in (3.2) and (3.4) as:
Varinter Varintraj
= Var
P
Can+Var P US 2Varj P
!0
B @
1 2(Var
P
C a n) 0:5
(Var P
U S) 0:5
Var P
C a n+VarU SP Correl
inter 1 Correlintraj
1 C
A: (3.5)
In obtaining expression (3.5), we used the analogous expression (3.3) for Varintra
j given by
Varintra
j =2Varj P 1 Correl Pintra
j , where Correlintraj denotes the correlation of price changes
between the various pairs of regions in country j. Given that in our data Var P
j is roughly
equal in the U.S. and Canada, di¤erences in inter- and intra-national RER volatilities are mainly accounted for by di¤erences in the correlation of price changes within and across countries.
Tables 4 and 5 report the values of Correlintraj and Correlinter for our various sets of
products. Note that in all cases, prices are more correlated within Canada than within the U.S., and prices are more correlated within countries than across countries. For example, based on the broad set of product matches for all exported products (Rows 1 and 2, Panel A in Table 4), Correlintra
Can = 0:85, CorrelintraUS = 0:76, and Correlinter = 0:06.
Hence, understanding why pricing-to-market is more prevalent across countries than within countries amounts to understanding why producers set prices that are less correlated across countries than within countries.
3.3. Additional robustness checks
Table 5 reports our statistics on product-level RERs if we change our baseline procedure along other dimensions. First, we construct our measure of product-level RERs net of movements in the category-wide RER (Panel D). Our …ndings on product-level RERs are roughly unchanged relative to our baseline results, highlighting the large extent of pricing-to-market that is idiosyncratic to individual products. Our …ndings on product-level RERs are also roughly unchanged if we construct movements in product-level RERs net of movements in nominal wages in each country, as in Engel and Rogers (1996), or if we de…ne product-level RERs as ratios of nominal prices without converting them into a common currency.
Second, we construct our statistics based on weekly wholesale prices instead of average weekly prices within a quarter (Panels E and F). Relative prices based on weekly data are even more volatile than when based on quarterly data. For all exported broad (identical) product matches, the international standard deviation of product-level RERs is 26% (33%)
using weekly data and 13% (11%) using quarterly data. Hence, pricing-to-market is more prevalent if we measure it using weekly prices. This is basically driven by the presence of sales and promotions (even at the wholesale level), which lead to temporary movements in prices.
Third, we construct our statistics based on retail prices instead of wholesale prices (Panels G and H). As discussed above, retail prices change less frequently than wholesale prices. However, movements in product-level RERs based on retail prices are also very large and three to four times as volatile as relative unit labor costs.
Finally, we consider two additional variations in the geographic scope of our statistics (due to space limitations, these are available upon request). First, we calculate international RERs based on single pricing regions in British Columbia and Seattle, Washington. Given the geographic closeness of these two districts, it is very likely that goods consumed in these pricing regions with a common country-of-origin are actually produced in the same location (and hence, share a common change in marginal cost). Second, we calculate our statistics based on single pricing regions in British Columbia and Manitoba in Canada, and Northern California and Illinois in the U.S. By using prices from single pricing regions in these larger geographical areas of Canada and U.S., we make sure that our intra-national price …ndings are not driven by sampling prices from nearby pricing regions in each country. Our …ndings are largely unchanged to these variations in geographic coverage.
4. Model
In what follows we present a simple framework that allows us to isolate key forces to rational-ize our empirical …ndings on prices. Since price stickiness has a limited role in accounting for movements in quarterly RERs in our data, we focus on models in which changes in markups stem from desired movements in markups and not from sticky prices in the currency of the buyer. The model encompasses a number of widely-used static models of international pric-ing with variable markups includpric-ing Kimball non-CES aggregator (Kimball 1995, Klenow and Willis 2006, Gopinath and Itskhoki 2010 and 2011), distribution costs (Corsetti and Dedola 2008), and nested-CES with a …nite number of products per sector (Atkeson and
Burstein 2007 and 2008).23 We use this model to understand the mechanisms that can rationalize our main empirical …ndings on RERs for traded goods produced in a common location and sold in multiple destinations: (i) product-level RERs are very volatile across regions in di¤erent countries,(ii)they are more volatile across regions in di¤erent countries than within countries, (iii) aggregate RERs comove closely with relative unit labor costs, and (iv) they move much more across regions in di¤erent countries than within countries.
Our model is partial equilibrium in that we take as given movements in wages and exchange rates. This is without loss of generality for the model’s pricing implications given a …xed set of goods. We do not address in this paper the general equilibrium question of what shocks lead to these large and persistent changes in relative labor costs across countries.
Notation All nominal prices are expressed in the currency of the region where the good
is sold. The logarithm of the producer price at timet of productn produced in regioni and sold in region r is denoted by pnirt.24 This price can expressed as the sum of log marginal
cost (mcnirt) and log gross markup ( nirt):
pnirt = nirt+mcnirt.
The log change of the price, pnirt, is given by:
pnirt = mcnirt+ nirt: (4.1)
The log change in the price of product n in region r (produced in region i) relative to the price in region r0 (produced in regionj) is:
qnijrr0t= ( mcnirt+ err0t mcnjr0t) + nirt njr0t . (4.2)
Movements in product-level RERs are accounted for by changes in relative markups between regions and by changes in relative marginal costs of supplying each region. If good n is produced in the same location i for sales in regions r and r0, assuming that the change in 23In the class of models we consider, the markup depends on a …rm’s price relative to the aggregate price.
Arkolakis, Costinot, Donaldson, and Rodriguez-Clare (2012) and references therein consider a class of static pricing models in which markups depend on the di¤erence between a …rm’s price and a “choke price” at which quantity is zero. The show under some assumptions that changes in the choke price are equal to a trade-weighted average of wage changes, very similar to changes in the aggregate price in our framework. Hence, this two class of models have similar implications for pricing-to-market.
24While we focus on producer prices, incorporating into the model a local wholesale distribution cost is
straightforward. Since wholesale gross margins represent a modest share of wholesale sales (on average16% for U.S. groceries and related products, as discussed above), this force can only account for a small fraction of the overall change in aggregate RERs in response to a change in relative unit labor costs.
marginal cost of supplying both regions is equal (so the …rst term in (4.2) is zero), then the change in the product-level RER is given by the change in relative markups between regions:
qniirr0t= nirt nir0t:
For goods that are not produced in the same location, changes in product-level RERs re‡ect changes in relative markups and marginal costs across locations.
Marginal Costs To study the determination of markup movements across regions, we
impose some additional structure on markups and marginal costs. The log of marginal cost is equal to the sum of the bilateral trade cost between the production location i and the destination r, ir 0 (with ii = 0), the wage in location i in period t expressed in region
r’s currency (wit+eirt), and a product-speci…c idiosyncratic cost component, znit:
mcnirt= ir+wit+eirt+znit.
In order to calculate expressions for the variance of product-level RERs, we assume thatznit
is independently, normally distributed across products and regions, withznit N(znit; 2z=2).
Abstracting from movements over time in bilateral trade costs, the log change in marginal cost in periodt is:
mcnirt = wit+ eirt+ znit, (4.3)
where znit is normally distributed with mean zero and variance 2z. Changes in average
relative costs across regions are driven by changes in relative wages expressed in the same currency, wit+ eirt wrt.
Markups We assume that the mark-up of productn in region r is a function of its price
relative to the aggregate price in regionr,pnirt prt, and an exogenous shock to the markup,
anirt, that we refer to asdemand shifter. That is, nirt = (pnirt prt; anirt). In the appendix
we describe three widely-used models of international pricing that produce this reduced-form relationship between markups, relative prices, and exogenous demand shifters, where the exact speci…cation of (:; :)and prt depends on model details.
The aggregate price prt is, up to a …rst-order approximation, an expenditure-weighted
average of log prices (adjusted for demand shiftersanirt) over all varieties sold in the region.
We assume thatanirtis distributed independently across products and time, but is potentially
variance-covariance matrix given by 2a a;rr0=2, with a;rr = 1. Hence anirt is normally
distributed with mean 0and variance-covariance matrix 2
a a;rr0.25
We now solve for changes in RERs, up to a …rst-order approximation, around a non-stochastic equilibrium. In anon-stochastic equilibrium, regions are ex-ante symmetric (err0 =
0andwi =wr for all countries and regions) and 2z = 2a= 0so that each product’s marginal
cost and demand shifter is at its average, i.e. mcnir = ir +zni and anir =anir.
Up to a …rst-order approximation, the log-change in markup is:
nirt= p;nir( prt pnirt) + a;nir anirt. (4.4)
where p;nir @(p@nir(:;:)pn) is the elasticity of the mark-up with respect to the relative price
evaluated at prices in the non-stochastic equilibrium, and a;nir @@anir(:;:)
nir is the elasticity of
the mark-up with respect to the demand shifter evaluated in the non-stochastic equilibrium. We make the following assumptions on p;nir and a;nir, which are satis…ed under some
parameter restrictions in the three models described in the appendix.
Assumption on markups: (i)Markups are weakly decreasing in the relative pricepnir pr,
p;nir 0;(ii)markups are weakly increasing in the demand shifter a;nir 0;(iii)the price
elasticity of markups, p;nir, is weakly decreasing in the relative price pnir pr and weakly
increasing in the demand shifteranir.
These assumptions imply that, everything else the same, a …rm tends to set higher prices (relative to the aggregate pricepr), lower markups, and be subject to a lower markup
elasticity in locations in which marginal costs are high relative to its competitors. Similarly, a …rm tends to set lower prices, lower markups, and face a lower markup elasticity in locations in which the demand shifter is relatively low. This implies that a …rm producing in regioni selling in regionsiandr facing trade costs ir >0and/or a lower demand shifter in regionr
will tend to set lower markups and be subject to a lower markup elasticity in region r than in region i.
Changes in prices and real exchange rates Combining (4.1), (4.3), and (4.4), the log
change in price (in the destination currency) is: pnirt=
1 1 + p;nir
( znit+ wit+ eirt) +
a;nir
1 + p;nir
anirt+
p;nir 1 + p;nir
prt. (4.5) 25We have assumed that …rms can charge a di¤erent price by destination, and that it is technologically
infeasible for any third party to ship goods across regions or countries to arbitrage price di¤erentials. It can be shown for the models presented in the appendix that price di¤erences between two regions do not exceed the bilateral trade cost if di¤erences inanirt are not too large. Under this assumption, any agent facing the
The …rst term represents the change in price in response to a change in cost (including the idiosyncratic and aggregate components). Pass-through is lower the higher is the markup elasticity p;nir. The second term represents the change in price in response to an
idiosyn-cratic change in the demand shifter. Pass-through is lower the higher is the markup elasticity
p;nir and pass-through is higher the higher is a;nir. The third term represents the change
in price in response to a change in the aggregate price level in the region where the good is sold. Pass-through is higher, the higher is the markup elasticity p;nir.
Using (4.5), the change in product-level RER for good n produced in region i and sold in regions r,r0 is:
qniirr0t =
p;nir0
1 + p;nir0
p;nir 1 + p;nir
( znit+ wit) +
a;nir
1 + p;nir
anirt
a;nir0
1 + p;nir0
anir0t
+ p;nir
1 + p;nir
prt+
p;nir0
1 + p;nir0
( err0t pr0t), (4.6)
Product-level RERs move with changes in producer costs( znit+ wit)if the markup
elas-ticity di¤ers across the two regions. Product-level RERs move with changes in demand shifters( anirt and anir0t)if these are not perfectly correlated between regions or if markup
elasticities di¤ers across regions. Product-level RERs move with changes in aggregate prices in the region where the good is sold if changes in aggregate prices di¤er between regions ( prt+ err0t pr0t6= 0) or if markup elasticities di¤er between regions.
We are interested in examining the forces shaping the statistics that we report in the empirical section. We use (4.6) to derive expressions for the variance of product-level RERs and movements in aggregate RERs for goods produced in a common location. In deriving these expressions, we assume that there is a large number of products in the economy.
Product-level RERs: We …rst provide an expression for the variance of product-level
RERs abstracting from aggregate movements in wages and exchange rates (or, similarly, assuming that idiosyncratic shocks are much larger than aggregate shocks).
Suppose that wages and exchange rates are constant across all regions: wit= eirt = 0
for all i and r. Up to a …rst-order approximation, the variance of product-level RERs for goods produced in a common location iand sold in regions r and r0 is:
Var( qniirr0t) = zirr0 2z+ a
irr0 2a, (4.7)
where
z irr0 =
Z n2 irr
1
j irrj
p;nir0
1 + p;nir0
p;nir
1 + p;nir
2
